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"We can think of each layer’s learned representation as a three-dimensional cube. Each cell in the cube is an activation, or the amount a neuron fires. The x- and y-axes correspond to positions in the image, and the z-axis is the channel (or detector) being run."

Furthermore, they offer a diagram which super-imposes the cube of Layer4a over the input image with the (x,y) axis overlaying the image itself.

I understand that the Neuron Objective is the input image that produces the highest activation for Layer 4a, Unit 11 which can be found at index=[11,0,0] of Layer 4a output=[14,14,512]. In this case, (x,y)=[11,0]. Each [1,1,480] kernel generates a feature map of shape=[14,14,1] with a total of 196 activations.

kernel => channel or feature map and activation => neuron or feature.

Question

But what is the intuitive concept of the (Positive) Channel Objective? In this example, Unit 11 sits in the same channel as 14x14=196 other neurons, but the channel objectives for all these neurons are different. If the optimized image for the Channel Objective maximizes the sum of neuron activations for channel 0, (e.g. slice=[14,14,0] of 192 1x1 convolutions or 512 total layer 4a channels) wouldn't it be the same for all 192 neurons in the same channel? Obviously, by the examples we see this is not true.

How does the Channel Objective relate to the Neuron Objective for Unit 11?

ANSWER

I understand that the Neuron Objective is the input image that produces the highest activation for Layer 4a, Unit 11 which can be found at index=[11,0,0] of Layer 4a output=[14,14,512].

This is where my understanding went off the rails. Layer 4a Unit 11 is actually channel/feature 12 of 192 for the 1x1 convolution. It is NOT the 12 of 196 neuron of channel 1. My fault for confusing 192 channels with 196 neurons/channel.

Instead, as mentioned the in answer, Unit 11 is a single neuron in channel 11, usually located near the center, e.g. Neuron Objective is (x,y,z)=(7,7,11) and Channel Objective is (x,y,z)=(:,:,11)

$\begingroup$your explanation of the Channel Objective was my first guess, but my intuition was that Channel Objectives should be the same for all neurons in the same channel. A look at the appendix confirms that this is not the case. Can you explain why?$\endgroup$
– michaelSep 11 '19 at 7:45

$\begingroup$@michael: I'm not sure that I follow? The appendix has one entry per channel. Do you mean the channel diversity visualizations?$\endgroup$
– Christopher OlahSep 11 '19 at 16:00

$\begingroup$now that you put it that way, dooh! I updated the question with my understanding of your Answer. But can you tell me if the position of the neuron was manually selected for clarity (relative to the Channel Objective), or pre-determined by some algorithm?$\endgroup$
– michaelSep 12 '19 at 1:13

$\begingroup$The default is to pick the middle position. But it doesn't really matter, as long as it isn't a the boundary of your image. It should look the same regardless of position.$\endgroup$
– Christopher OlahSep 13 '19 at 19:38